write an explicit definition for the sequence -4,1,6,11,....

write an explicit definition for the sequence -4,1,6,11,....

$$\\\small{\text{arithmetical sequence: $d = 5$ and $a_1 = -4$ }}\\\\ \small{ \begin{array}{rclclcr} a_1 &=& -4 \\ a_2 &=& a_1 + 1\cdot 5 &=& -4 + 5 &=& 1\\ a_3 &=& a_1 + 2\cdot 5 &=& -4 + 10 &=& 6\\ a_4 &=& a_1 + 3\cdot 5 &=& -4 + 15 &=& 11\\ \cdots \\ \mathbf{a_n }& \mathbf{=} & \mathbf{a_1 + (n-1)\cdot d \\\\ a_n &=& -4 + (n-1) \cdot 5 \\ a_n &=& -4 + 5\cdot n - 5 \\ a_n &=& -4-5 + 5\cdot n \\ \mathbf{a_n }& \mathbf{=} & \mathbf{-9 + 5\cdot n } \\ \\ \hline \end{array} }\\$$

$$\\\small{\text{check:}}\\ \small{\text{$ \begin{array}{rcl} a_4 &=& -9+5\cdot 4\\ a_4 &=& -9 + 20 \\ a_4 &=& 11 \qquad \text{ okay } \\\\ \end{array} $}}$$